Example $4$

Air as an ideal gas, flows through a well$-$insulated turbine $($where the effects of kinetic and

potential energy are neglected$).$ Specific heat is assumed to be constant at $1\mathrm{.}005K\frac{J}{k}{g}^{***}K.$

You know the following equation is used to find the specific work produced by the turbine:

$=cp(T_1-T_2)$

You also know the temperatures and the uncertainty of the thermocouples used to measure

the temperature of the air:

$T_1=1200K+-0\mathrm{.}05K$

$T_2=500K+-0\mathrm{.}05K$

Calculate the uncertainty and relative uncertainty in the specific work for the turbine.

Provide the uncertainty in the following format Nominal $+-$ uncertainty.